This paper presents a theoretical design study of a transcritical CO2 heat pump system for simultaneous cooling and heating. The heat pump model consists of the components: compressor, internal heat exchanger, valve, evaporator and gas cooler. The evaporator and the gas cooler are both water coupled intended for district cooling and heating respectively. Initially a thermodynamic cycle analysis has been done on the system followed by a heat transfer analysis of the heat exchangers using finite difference models. The main subject of this paper is an investigation of the effects that parameter uncertainties have on the design results: thermodynamic performance expressed by coefficient of performance (COP) and heat exchanger sizes expressed by weight. The parameters to be investigated are the compressor isentropic efficiency, effectiveness of the internal heat exchanger and pressure drops in the heat exchangers. The results show that COP is particular sensitive to the pinch temperature in the gas cooler and to the compressor isentropic efficiency but not to pressure loss. However it is found that the heat exchanger weights are very sensitive to pressure loss. The thermodynamic and heat exchanger models proposed in this study are self-contained and forms the basis for an economic analysis and optimization in future work.